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Age 11 to 14
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  • Problem
  • Student Solutions

You can draw 1, 2, 3, 7, 8, 9 and 11 without taking your pen off the paper.

Why?

Nodes are places where two or more lines meet. On these diagrams, the nodes are clearly shown by the black points.

If a node has an even number of lines coming from it, this means that your pen will be able to both enter and leave that node.

If not, the pen must start or finish at the node.

As you can start and finish at only two nodes (start at one, finish at the other), if the diagram has more than two nodes with odd numbers of lines, you won't be able to draw it without taking your pen off the paper.

If all the nodes have even numbers of lines, then you can draw the diagram without taking your pen off the paper and starting and finishing at the same place.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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